{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T23:56:19Z","timestamp":1768866979773,"version":"3.49.0"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T00:00:00Z","timestamp":1768780800000},"content-version":"vor","delay-in-days":18,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100018786","name":"Al-Zaytoonah University of Jordan","doi-asserted-by":"publisher","award":["32\/13\/2024-2025"],"award-info":[{"award-number":["32\/13\/2024-2025"]}],"id":[{"id":"10.13039\/501100018786","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:p>In this paper, we model edge traffic with a conformable fractional partial differential equation that keeps memory in time and space. The solution represents a unit\u2010free attack pressure, built from a z\u2010scored edge series, a quiet period baseline, and a partially absorbing boundary that reflects scrubbing and rate limits. Using a closed form atomic solution, we split the edge signal into a growth part and a damped part for early warning, and use a simple spatial factor to estimate how far pressure can travel inside. The result is a small, readable model that turns one edge metric into clear, tier\u2010specific actions during DDoS attacks.<\/jats:p>","DOI":"10.1155\/jama\/4338391","type":"journal-article","created":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T11:31:05Z","timestamp":1768822265000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Early Detection of Cyberattacks in Banking Networks via a Fractional Partial Differential Equation Model"],"prefix":"10.1155","volume":"2026","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-0940-828X","authenticated-orcid":false,"given":"Ahmad","family":"Alshanty","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6403-3448","authenticated-orcid":false,"given":"Waseem Ghazi","family":"Alshanti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0838-4382","authenticated-orcid":false,"given":"Amjed","family":"Zraiqat","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,1,19]]},"reference":[{"key":"e_1_2_11_1_2","doi-asserted-by":"publisher","DOI":"10.1145\/205447.205464"},{"key":"e_1_2_11_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/90.392383"},{"key":"e_1_2_11_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/90.650143"},{"key":"e_1_2_11_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0370-1573(00)00070-3"},{"key":"e_1_2_11_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/90.282603"},{"key":"e_1_2_11_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/49.400651"},{"key":"e_1_2_11_7_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/047120644X","volume-title":"Self-Similar Network Traffic and Performance Evaluation","author":"Park K.","year":"2000"},{"key":"e_1_2_11_8_2","first-page":"162","volume-title":"Proceedings of the IEEE Canadian Conference on Electrical and Computer Engineering","author":"Liu J.","year":"1999"},{"key":"e_1_2_11_9_2","first-page":"27","volume-title":"A Practical Guide to Heavy Tails: Statistical Techniques and Applications","author":"Willinger W.","year":"1998"},{"key":"e_1_2_11_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2014.01.002"},{"key":"e_1_2_11_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cose.2004.04.005"},{"key":"e_1_2_11_12_2","first-page":"725","article-title":"Atomic Solution of Certain Inverse Problems","volume":"3","author":"Khalil R.","year":"2010","journal-title":"European Journal of Pure and Applied Mathematics"},{"key":"e_1_2_11_13_2","doi-asserted-by":"publisher","DOI":"10.58997\/ejde.2024.28"},{"key":"e_1_2_11_14_2","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1090\/S0002-9904-1978-14524-8","article-title":"Vector Measures","volume":"84","author":"Diestel J.","year":"1978","journal-title":"Bulletin of the American Mathematical Society"},{"key":"e_1_2_11_15_2","doi-asserted-by":"publisher","DOI":"10.1080\/01630568608816217"},{"key":"e_1_2_11_16_2","doi-asserted-by":"publisher","DOI":"10.15849\/IJASCA.220720.08"},{"key":"e_1_2_11_17_2","doi-asserted-by":"publisher","DOI":"10.15849\/IJASCA.220720.07"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/4338391","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/4338391","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/4338391","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T11:31:11Z","timestamp":1768822271000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/4338391"}},"subtitle":[],"editor":[{"given":"Roberto G.","family":"Ram\u00edrez-Chavarr\u00eda","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["10.1155\/jama\/4338391"],"URL":"https:\/\/doi.org\/10.1155\/jama\/4338391","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1]]},"assertion":[{"value":"2025-10-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-12-10","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-01-19","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"4338391"}}